Question - Lolita, an intelligent and charming Holstein cow, consumes only two goods, cow feed (made of ground corn and oats) and hay. Her preferences are represented by the utility function U(x, y) = x - x2/2+y, where x is her consumption of cow feed and y is her consumption of hay. Lolita has been instructed in the mysteries of budgets and optimization and always maximizes her utility subject to her budget constraint. Lolita has an income of $m that she is allowed to spend as she wishes on cow feed and hay. The price of hay is always $1, and the price of cow feed will be denoted by p, where 0 < p ≤ 1.
(a) Write Lolita's inverse demand function for cow feed.
(b) If the price of cow is p and her income is m, how much hay does Lolita choose?
(c) Plug these numbers into her utility function to find out the utility (c) level that she enjoys at this price and this income.
(d) Suppose that Lolita's daily income is $3 and that the price of feed is 8.50. What bundle does shy buy? What bundle would she buy if the cow feed rose to $1?